Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "8.24" was replaced by "(824/100)".

Step  1  :

 1.1     10 = 2•5

(10)^-5 = (2•5)^(-5) = (2)^(-5) • (5)^(-5)

Equation at the end of step  1  :

  824
  ——— • ((2)(-5)•(5)(-5))
  100

Step  2  :

            206
 Simplify   ———
            25 

Equation at the end of step  2  :

  206
  ——— • ((2)(-5)•(5)(-5))
  25 

Step  3  :

Multiplying exponents :

 3.1    5²  multiplied by  5⁵   = 5^{(2 + 5)} = 5⁷

Dividing exponents :

 3.2    2¹   divided by   2⁵   = 2^{(1 - 5)} = 2^(-4) = ¹/_2⁴

Final result :

    103             
  ——————— = 0.00008 
  (57•24)